State Complexity of Basic Operations on Nondeterministic Finite Automata

  • Markus Holzer
  • Martin Kutrib
Conference paper

DOI: 10.1007/3-540-44977-9_14

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2608)
Cite this paper as:
Holzer M., Kutrib M. (2003) State Complexity of Basic Operations on Nondeterministic Finite Automata. In: Champarnaud JM., Maurel D. (eds) Implementation and Application of Automata. CIAA 2002. Lecture Notes in Computer Science, vol 2608. Springer, Berlin, Heidelberg


The state complexities of basic operations on nondeterministic finite automata (NFA) are investigated. In particular, we consider Boolean operations, catenation operations - concatenation, iteration, λ- free iteration - and the reversal on NFAs that accept finite and infinite languages over arbitrary alphabets. Most of the shown bounds are tight in the exact number of states, i.e. the number is sufficient and necessary in the worst case. For the complementation tight bounds in the order of magnitude are proved. It turns out that the state complexities of operations on NFAs and deterministic .nite automata (DFA) are quite different. For example, the reversal and concatenation have exponential state complexity on DFAs but linear complexity on NFAs. Conversely, the complementation can be done with linear complexity on DFAs but needs exponentially many states on NFAs.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Markus Holzer
    • 1
  • Martin Kutrib
    • 2
  1. 1.Institut für InformatikTechnische Universität MünchenMünchenGermany
  2. 2.Institut für InformatikUniversität GiessenGiessenGermany

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